A nonlinear wiener process degradation model with damage resistance for reliability analysis

Abstract

Systems commonly experience competing risks of internal degradation and random shocks. Random shocks may cause damage to the system, and the degrees of the damage affect system degradation differently. In this paper, we consider a system, namely, a damage-resistant system, designed to withstand shocks up to a specified threshold. To consider the system damage resistance, we first propose a new shock classification based on the shock magnitude and define the damage resistance level of the system accordingly. Furthermore, because the system will be more vulnerable to shocks over time, we divide the system degradation process into two stages and propose nonlinear Wiener process degradation models with two stages by incorporating the system damage resilience level with the new shock classification. The closed-form system reliability functions for these two stages are further derived. Lastly, we conduct numerical examples with real-world data to demonstrate the practical application of our proposed model.